Graph this system of equations and solve. $y = -\dfrac{6}{5} x - 1$ $y = -2 x - 5$ 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 Click and drag the points to move the lines.
The y-intercept for the first equation is $-1$ , so the first line must pass through the point $(0, -1)$ The slope for the first equation is $-\dfrac{6}{5}$ . Remember that the slope tells you rise over run. So in this case for every $6$ positions you move down (because it's negative) You must also move $5$ positions to the right. $5$ positions to the right. $6$ positions down from $(0, -1)$ is $(5, -7)$ Graph the blue line so it passes through $(0, -1)$ and $(5, -7)$ The y-intercept for the second equation is $-5$ , so the second line must pass through the point $(0, -5)$ The slope for the second equation is $-2$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move down (because it's negative) You must also move $1$ positions to the right. $1$ position to the right. $2$ positions down from $(0, -5)$ is $(1, -7)$ Graph the green line so it passes through $(0, -5)$ and $(1, -7)$ The solution is the point where the two lines intersect. The lines intersect at $(-5, 5)$.